Question

Rút gọn:

a) \(A=100^2-99^2+98^2-97^2+...........+2^2-1^2\)

b) \(B=3\left(2^2+1\right)\left(2^4+1\right)................\left(2^{64}+1\right)+1\)

c) \(C=\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a+b\right)^2\)

Mọi người giúp mình với, làm được câu nào thì làm nha, xin hãy quan tâm.

Answer 1

\(A=100^2-99^2+98^2-97^2+...+2^2-1^2\)

\(A=\left(100^2-99^2\right)+\left(98^2-97^2\right)+...+\left(2^2-1^2\right)\)

\(A=1.199+1.195+...+3.1\)

\(A=3+7+...+195+199\)

Tổng A có: \(\frac{199-3}{4}+1=50\)( số hạng)

\(\Rightarrow A=\frac{\left(199+3\right).50}{2}=5050\)

Mấy ý kia chốc về lm nốt 

Answer 2

\(B=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)

\(B=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)

\(B=\left(2^8-1\right)...\left(2^{64}+1\right)+1\)

\(B=2^{64}-1+1\)

\(B=2^{64}\)

Answer 3

\(C=\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a+b\right)^2\)

Đặt \(a+b=t\)

\(\Rightarrow C=\left(t+c\right)^2+\left(t-c\right)^2-2t^2\)

\(C=t^2+2tc+c^2+t^2-2tc+c^2-2t^2\)

\(C=2c^2\)